deletions | additions       diff --git a/Splitting the Num.tex b/Splitting the Num.tex  index d0c646e..208aff0 100644  --- a/Splitting the Num.tex  +++ b/Splitting the Num.tex 
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\end{equation}  which are $\theta=0,180$ which correspond to the normal number line, (both components fold in) and the mod of the number line $|n \in \mathbb{R}|$ (the normal negative component folds onto the real part).  There exist non symmetric solutions to the equation \begin{equation}  4 = \Bigg[ \frac{cos^2(\theta)+2cos(\theta)cos(\varphi)+cos^2(\varphi)}{cos^2(\theta)cos^2(\varphi)}\Bigg]  \end{equation}  A suggested Cayley table by D.Worthy is  \begin{equation} 
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\end{array}  \end{equation}  There is a suggested set of angles in which $\theta=\varphi=\frac{\pi}{3}$ for symmetric properties by R.Garner. These appear to only be 0 and 180 degree angles.  If one required the numbers to be held on the complex plane then the basis elements are \begin{equation}  \hat{e_{-}} = -\hat{e_{+}}\exp(i\theta) \\